Book/Report

FZJ-2018-00723

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Displacement correlation of classical ions in the incommensurate Fröhlich model of a one- dimensional metal

Eisenriegler, E. (Corresponding author)FZJ*

1976
Kernforschungsanlage Jülich, Verlag Jülich

Please use a persistent id in citations: http://hdl.handle.net/2128/16674

Report No.: Juel-1337

Abstract: The one-dimensional Fröhlich model is investigated for k$_{B}$T $\ll$$\delta_{o}$ $\ll$E$_{F}$ with $\delta_{o}$ the mean field Peierls gap at T = O. Treating the ions classically and neglceting bandstructure and Umklapp effects the electronic energy for a given ion distortion is determined by Bogolyubov-type equations with a $\underline{complex}$ order parameter. For $\vert$p$\vert$$\gg$$\delta_{o}$/v$_{F}$ (p is the waveveetor deviation from 2k$_{F}$ ) the (electron-renormalized) phonons are shown to be harmonie with a universal dispersion curve, i.e. independent of T and the possible presence of long wavelength ($\vert$p$\vert$<$\delta_{o}$/v$_{F}$ ) phonon excitations. For an infinitely long ranged Peierls distortion the harmonic phonon excitations are calculated for arbitrary wavevector and temperature. If $\vert$p$\vert$<$\delta_{o}$/v$_{F}$, one obtains a mixing and energy splitting of the two phonons 2k$_{F}$+p and -2k$_{F}$+p leading to the so-called harmonic phase and amplitude modes. This phonon coupling decreases rapidly for $\vert$p$\vert\gtrsim \delta_{o}/v_{F}$ and both dispersions merge into the universal dispersion. The long wavelength ($\vert p \vert < \delta_{o}/v_{F}$) phonon excitations in general are described approximately by a Ginzburg-Landau (GL) energy functional where the important fluctuations ocur in the phase of the order parameter. For wavelengths small compared to the GL phase-coherence length ($\vert p\vert \gg k_{B}T/v_{F}$), the $\underline{harmonic}$ phase (and amplitude) mode become well defined modes and determine the correlation function. Actually, the GL and harmonic results for the correlation function coincide for k$_{B}$T/v$_{F} \ll \vert p \vert \ll \delta_{o} /v_{F}$ leading order in the small quantity k$_{B}$T/$\delta_{o}$. The theory is compared with X-ray and neutron scattering experiments on KCP.

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Contributing Institute(s):

1. Publikationen vor 2000 (PRE-2000)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

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